How to Determine Cubic Yards: 11 Steps

2024 Author: Samantha Chapman | [email protected]. Last modified: 2024-02-02 02:12

The cubic yards (abbreviated "yd³"or" cu yd ") are a volumetric unit of measurement that corresponds to the volume of a cube whose sides measure exactly 1 yard, or approximately 764.5 liters. Cubic yards are the preferred unit of measurement for a variety of practical tasks and activities - such as pouring concrete during a construction project. For a given rectangular area with length "L", width "W", and height "H", a volume in cubic yards can be calculated simply through the equation Volume = L x W x H, assuming that L, W, and H are measured in yards.

Steps

Method 1 of 2: Method: Determine the Volume of Three Dimensional Areas

Step 1. Collect all necessary yardage measurements

Volumes in cubic yards can be calculated relatively easily for a variety of standard three-dimensional areas, thanks to a few simple equations. However, these equations require that all measurements be expressed in yards. Therefore, before using any of these equations, it is important to make sure that you have taken the initial measurements in yards or, alternatively, that they have been converted to yards using a conversion factor. Here are some more common length measurement conversions:

• 1 yard = 3 feet
• 1 yard = 36 inches
• 1 yard = 0.914 meters
• 1 yard = 91.44 centimeters

Step 2. Use the L x W x H equation for rectangular areas

The volume of any three-dimensional rectangular area (rectangular prism, cuboid, etc.), can be determined simply by multiplying the length by the width, and the result obtained by the height. This equation can also be expressed as the surface area of one of the faces of the rectangular area multiplied by the dimension perpendicular to that surface.

• For example, let's say we want to determine the volume (in yd³) of the dining room of our house. We measure the dining room and get 4 yd in length, 3 yd in width and 2.5 yd in height. To determine the volume of the room, simply multiply its length, width and height:

  • 4 × 3 × 2, 5
  • = 12 × 2, 5
  • = 30. The room has a volume of 30 yd³.
  • Cubes are rectangular areas where all faces have the same length. Hence, the volume equation of a cube can be reduced from L x W x H to L³, etc.

  

  Step 3. For cylindrical areas, use the equation π × R² × H.

  To calculate the volume of a cylindrical space just multiply the two-dimensional area of one of its circular areas by the height or length of the cylinder. Calculate the area of the circular surface of the cylinder using the equation used to determine the surface of the circles: multiply the mathematical constant π (3, 1415926 …) by the radius of the circle (the distance from the center of the circle to one of the points on the circumference) multiplied by itself. So, to find the volume of the cylinder, simply multiply the value obtained by the height of the cylinder. As always, make sure all values are in yards

  • For example, let's say we want to determine the volume of a cylindrical hole in our back patio before installing a fountain. The hole is 1.5 yards in diameter and 1 yard deep. Divide the diameter of the hole by two to get its radius: 0.75 yards. Then, multiply the variables using the cylinder volume equation:

    • (3, 14159) × 0, 75² × 1
    • = (3, 14159) × 0, 5625 × 1

    • = 1,767. The hole has a volume of 1, 767 yd³.

      

      Step 4. For spheres, use the equation 4/3 π × R³.

      To calculate the volume of a sphere in cubic yards, all you need to know is its radius - the distance from the center to a point on the circumference - in yards. Simply cube this number (multiply it by itself twice), then multiply it by 4/3 π to get the volume of the sphere in cubic yards.

      • For example, let's say we want to calculate the volume of a spherical balloon. The air balloon is 10 yards in diameter. Divide the diameter by two to find the radius of the balloon - 5 yards. Next, just substitute this value for "R" in the equation as follows:

        • 4/3 π × (5)³
        • = 4/3 (3, 14159) × 125
        • = 4, 189 × 125
        • = 523.6. The balloon has a volume of 523 0, 6 yd³.

        

        Step 5. For cones, use the equation 1/3 π × R² × H.

        The volume of a given cone is 1/3 of the volume of a cylinder which has the same height and radius as the cone. Just calculate the height and radius of a cone (in yards), then solve the equation as if you were calculating the volume of a cylinder. Multiply the result by 1/3 to get the volume of the cone.

        • For example, let's say we want to calculate the volume of an ice cream cone. The ice cream cone is quite small - it has a radius of 1 inch and a height of 5 inches. After converting these measurements to yards, we get 0, 028 yards and 0, 139 yards, respectively. Solve as follows:

          • 1/3 (3, 14159) × 0, 028² × 0, 139
          • = 1/3 (3, 14159) × 0, 000784 × 0, 139
          • = 1/3 × 0, 000342
          • = 1, 141^-4. The ice cream cone has a volume of 1, 141^-4 yd³

          

          Step 6. For irregular shapes try using more equations

          To calculate the volume of a three-dimensional shape that does not have a standard equation, try to dissect the area into multiple surfaces, this way its volume (in cubic yards) can be calculated more easily. Then, calculate the volume of these surfaces individually, adding the results to find the final volume value.

          • Let's say, for example, we want to calculate the volume of a small grain silo. The silo has a cylindrical body with a height of 12 yards and a radius of 1.5 yards. The silo also has a 1 yard high conical roof. By calculating the volume of the roof and the silo body separately, we get the total volume of the silo:

            • π × R² × H + 1/3 π × R '² × H '
            • (3, 14159) × 1, 5² × 12 + 1/3 (3, 14159) × 1, 5² × 1
            • = (3, 14159) × 2, 25 × 12 + 1/3 (3, 14159) × 2, 25 × 1
            • = (3, 14159) × 27 + 1/3 (3, 14159) × 2, 25
            • = 84, 822 + 2, 356
            • = 87, 178. The total volume of the silo is 87, 178 cubic yards.

            Method 2 of 2: Method Two: A Quick Trick to Determine the Yards of Concrete Areas

            

            Step 1. Determine the square feet of the area where you are pouring the concrete

            When casting to create, for example, a concrete patio, the concrete is usually poured into a mold with a thickness that can range from a few inches to a foot. In this case it is not necessary to use relatively complex formulas to determine the volume of concrete you will need. Instead, use this simple trick to quickly calculate how much concrete you need. Start by calculating the square feet of the area you are pouring into.

            • Remember - square feet need to be in feet and not yards.

            • As a reminder, the area of squares and rectangles can be calculated by multiplying Length x Width. For circles the formula is π × R².

              For more complex shapes, visit the wikiHow article other articles on how to calculate surface area.

            

            Step 2. Calculate the required thickness of the concrete

            It's simple - just measure the depth of the mold you're pouring into. Since we are pouring into a relatively shallow mold, and since calculating fractions of feet can be cumbersome during the process, we can take our measurements directly in inches.

            

            Step 3. Divide the square feet by a coefficient based on the thickness of the concrete

            All you have to do to determine the yardage of the concrete is to divide the number of square feet by a certain value; if the concrete has to be thin this value will be bigger, if the concrete has to be thick this value will be smaller. Read the most commonly used thicknesses below, or proceed to the next step if the thickness does not correspond to one of the values shown:

            • If the concrete is 4 inches thick, divide the square feet by 81 to determine cubic yards.
            • If the concrete is 6 inches thick, divide the square feet by 54 to determine cubic yards.
            • If the concrete is 8 inches thick, divide the square feet by 40 to determine cubic yards.
            • If the concrete is 12 inches thick, divide the square feet by 27 to determine cubic yards.

            

            Step 4. Determine uneven thicknesses using a simple formula

            If you have a thickness that doesn't match any of the examples above, don't worry, it's easy to find the amount you need. Just divide 324 by the thickness of the concrete (in inches). Then multiply the answer by the square feet to determine the total square feet of the concrete.

            • Let's assume that the concrete for an area of 10 x 10 feet must be 3.5 inches thick. In this case, we would calculate the square feet as follows:

              • 324/3, 5 = 92, 6
              • 10 × 10 = 100
              • 100/92, 6 = 1, 08. We would need to 1, 08 yd³ concrete.

              

              Step 5. Purchase more concrete than you need

              When it comes to pouring concrete, it is usually a good idea to purchase more concrete in case the measurements taken are not accurate. After all, the concrete mix that remains unused can always be saved and used for another project. However, not having enough can be a problem - someone will have to rush to the hardware store before continuing work. So be sure to buy some more, especially for projects that require more.